find the value of x in the triangle shown below ​

Answer:

x = -2

y= -5

is the solution of the system of equations

Answer:

It will cost 42 to completely fill the box with hay.

have a good day <3

Answer:

Step-by-step explanation:

If you meant " | ", as in |x|, that's "absolute value."  The domain of this function is "all real numbers," and the range is "all real numbers zero or greater."

Answer:7.3

Step-by-step explanation:

hypotenuse=h=16

Adjacent=x

Φ=63°

CosΦ=x/h

Cos63=x/16

Cross multiply

16 x cos63=x

Cos63=0.4540

16 x 0.4540=x

7.3=x

x=7.3

Answer:

E) Because the interval contains 0, it is possible that there is no difference in mean carbonation levels.

Step-by-step explanation:

Hello!

The soda manufacturer claims that it's Cherry Fizz soda that has more carbonation than the competitor's Cherry Eclipse soda.

To test this claim they compared the carbonation by opening bottles of each soda, covered them with a balloon, and agitated the bottle to release the gas into the ballon. Later the balloon's diameter of each bottle of soda was measured.

Be the variables:

X₁: Diameter of a balloon filled with the gas of a Cherry Fizz soda bottle.

X₂: Diameter of a balloon filled with the gas of a Cherry Eclipse soda bottle.

X[bar]₁= 2.3 inches

X[bar]₂= 2.1 inches

The difference between the two means μ₁-μ₂ was estimated with a 90% CI, obtaining: [-0.8;1.2]inches

Usings 90% confidence level you can expect the interval [-0.8;1.2]inches to include the difference between the diameter of the balloons filled with the gas of the Cherry Fizz soda and the diameter of the balloons filled with the gas of the Cherry Eclipse soda.

The claims are:

A) Because 2.3 inches is larger than 2.1 inches, the manufacturer is correct, and Cherry Fizz has more carbonation.

INCORRECT, the given values are sample measures, you cannot reach any valid conclusions by simply comparing them.

B) Because the interval has more positive than negative values, Cherry Fizz has more carbonation.

INCORRECT, the confidence interval provides a range of values for the estimated parameter, it is equally probable that the parameter is closer to the lower bond, the upper bond, or in the middle of the interval.

C) Because 2.3 and 2.1 are very similar, there is no difference in the mean carbonation levels.

INCORRECT, same as in item A, you cannot reach any valid conclusion by just comparing the sample values, a propper hypothesis test is needed.

D) The interval cannot be interpreted because negative measurements are not possible.

INCORRECT, this interval vas made to estimate the difference between the two means, therefore if one value is less than the other it is possible to observe negative values.

If the CI was to estimate the value of the mean diameter of the balloons of one of the groups, then a negative measurement would be invalid.

E) Because the interval contains 0, there may be no difference in mean carbonation levels.

CORRECT

If you were to test the hypotheses

H₀: μ₁-μ₂=0

H₁: μ₁-μ₂≠0

Using a significance level, complementary to the confidence level used to construct the interval α: 0.1 you can decide whether or not the difference between population means are equal to zero or not.

If the interval contains the zero, then you do not reject the null hypotheses and there is no difference between the population means.

If the interval doesn't include the zero, then you reject the null hypothesis.

I hope this helps!

E) Because the interval contains 0, it is possible that there is no difference in mean carbonation levels.

The soda manufacturer claims that it's Cherry Fizz soda that has more carbonation than the competitor's Cherry Eclipse soda.

To test this claim they compared the carbonation by opening bottles of each soda, covered them with a balloon, and agitated the bottle to release the gas into the ballon. Later the balloon's diameter of each bottle of soda was measured.

Be the variables:

X₁: Diameter of a balloon filled with the gas of a Cherry Fizz soda bottle.

X₂: Diameter of a balloon filled with the gas of a Cherry Eclipse soda bottle.

X[bar]₁= 2.3 inches

X[bar]₂= 2.1 inches

The difference between the two means μ₁-μ₂ was estimated with a 90% CI, obtaining: [-0.8;1.2]inches

Usings 90% confidence level you can expect the interval [-0.8;1.2]inches to include the difference between the diameter of the balloons filled with the gas of the Cherry Fizz soda and the diameter of the balloons filled with the gas of the Cherry Eclipse soda.

The claims are:

A) Because 2.3 inches is larger than 2.1 inches, the manufacturer is correct, and Cherry Fizz has more carbonation.

B) Because the interval has more positive than negative values, Cherry Fizz has more carbonation.

C) Because 2.3 and 2.1 are very similar, there is no difference in the mean carbonation levels.

D) The interval cannot be interpreted because negative measurements are not possible.

If the CI was to estimate the value of the mean diameter of the balloons of one of the groups, then a negative measurement would be invalid.

E) Because the interval contains 0, there may be no difference in mean carbonation levels.

Using a significance level, complementary to the confidence level used to construct the interval α: 0.1 you can decide whether or not the difference between population means are equal to zero or not.

If the interval contains the zero, then you do not reject the null hypotheses and there is no difference between the population means.

If the interval doesn't include the zero, then you reject the null hypothesis.

Thus the interval contains 0, it is possible that there is no difference in mean carbonation levels.

To know more about null Hypothesis follow

https://brainly.com/question/15980493

Answer:

a) 5.37% probability that an individual distance is greater than 210.9 cm

b) 75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c) Because the underlying distribution is normal. We only have to verify the sample size if the underlying population is not normal.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 197.5, \sigma = 8.3[/tex]

a. Find the probability that an individual distance is greater than 210.9 cm

This is 1 subtracted by the pvalue of Z when X = 210.9. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{210.9 - 197.5}{8.3}[/tex]

[tex]Z = 1.61[/tex]

[tex]Z = 1.61[/tex] has a pvalue of 0.9463.

1 - 0.9463 = 0.0537

5.37% probability that an individual distance is greater than 210.9 cm.

b. Find the probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

Now [tex]n = 15, s = \frac{8.3}{\sqrt{15}} = 2.14[/tex]

This probability is 1 subtracted by the pvalue of Z when X = 196. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{196 - 197.5}{2.14}[/tex]

[tex]Z = -0.7[/tex]

[tex]Z = -0.7[/tex] has a pvalue of 0.2420.

1 - 0.2420 = 0.7580

75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

The underlying distribution(overhead reach distances of adult females) is normal, which means that the sample size requirement(being at least 30) does not apply.

Answer:

[tex]\dfrac{14}{29}[/tex]

Step-by-step explanation:

Let P(A) be the probability that goggle of type A is manufactured

P(B) be the probability that goggle of type B is manufactured

P(E) be the probability that a goggle is returned within 10 days of its purchase.

According to the question,

P(A) = 30%

P(B) = 70%

P(E/A) is the probability that a goggle is returned within 10 days of its purchase given that it was of type A.

P(E/B) is the probability that a goggle is returned within 10 days of its purchase given that it was of type B.

[tex]P(A \cap E)[/tex] will be the probability that a goggle is of type A and is returned within 10 days of its purchase.

[tex]P(B \cap E)[/tex] will be the probability that a goggle is of type B and is returned within 10 days of its purchase.

[tex]P(E \cap A) = P(A) \times P(E/A)[/tex]

[tex]P(E \cap A) = \dfrac{30}{100} \times \dfrac{5}{100}\\\Rightarrow P(E \cap A) = 1.5 \%[/tex]

[tex]P(E \cap B) = P(B) \times P(E/B)[/tex]

[tex]P(E \cap B) = \dfrac{70}{100} \times \dfrac{2}{100}\\\Rightarrow P(E \cap B) = 1.4 \%[/tex]

[tex]P(E) = 1.5 \% + 1.4 \% \\P(E) = 2.9\%[/tex]

If a goggle is returned within 10 days of its purchase, probability that it was of type B:

[tex]P(B/E) = \dfrac{P(E \cap B)}{P(E)}[/tex]

[tex]\Rightarrow \dfrac{1.4 \%}{2.9\%}\\\Rightarrow \dfrac{14}{29}[/tex]

So, the required probability is [tex]\dfrac{14}{29}.[/tex]

Answer: 346.4 in^3

Step-by-step explanation:

The pot can be thinked as a cylinder:

The volume of a cylinder is equal to:

V = (pi*r^2)*h

where h is the height, r is the radius and pi = 3.1416

Here we have that: r = 3.5in, h = 9in.

Then the volume is:

V = 3.1416*(3.5in)^2*9in = 346.4in^3

Answer:

y=2x

Step-by-step explanation:

Every one x is two y.

Answer:

14

Step-by-step explanation:

7-5 = 2

4/2 = 2

2 x 7 = 14

Answer:

696.265 inches

Step-by-step explanation:

Radius = 27/2 = 13.5

2 semicircles + 2 lengths

(3.14 × 13.5²) + 2(62)

696.265 inches

Answer:

696

Step-by-step explanation:

Answer:

The range in shelter A is 22, and the range in shelter B is 18.

Subtract 8 from 30 shelter A which gives you 22. Then subtract 10 from 28 which gives you 18 for Shelter B.

Answer:

The range in shelter A is 22, and the range in shelter B is 18.

Subtract 8 from 30 shelter A which gives you 22. Then subtract 10 from 28 which gives you 18 for Shelter B.

Step-by-step explanation:

Answer:

3.508 kilograms

Step-by-step explanation:

This question can be solved using a rule of three.

We have that each kilogram is 1000 grams. How many kilograms are there for 3508 grams?

1kg - 1000g

xkg - 3508g

[tex]1000x = 3508[/tex]

[tex]x = \frac{3508}{1000}[/tex]

[tex]x = 3.508[/tex]

So the correct answer is:

3.508 kilograms

Answer:

20x + 30y = 680

Step-by-step explanation:

Give me a good rating please!

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The equation represents the number of $20 and $30 gift cards bought.

20x + 30y = 680

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Number of gift cards for $20 = x

Number of gift cards for $30 = y

Total amount spend on gift card = $680

The equation represents the number of $20 and $30 gift cards bought.

20x + 30y = 680

Thus,

The equation represents the number of $20 and $30 gift cards bought.

20x + 30y = 680

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ2

Answer:

  see below

Step-by-step explanation:

It is usually convenient to choose small exponents when graphing an exponential function. You can get a reasonable idea of the shape of the curve using x-values with a magnitude of 3 or less.

The exponential term 2^x has a horizontal asymptote of y=0 for large negative values of x. Adding 3 to that term shifts the horizontal asymptote up to y=3. Of course, everything else is shifted up the same amount.

You know that ...

  2^-1 = 1/2

  2^0 = 1

  2^1 = 2

  2^2 = 4

Adding 3 to these values will give you points on the graph for x=-1 to 2.

Answer:

Option C

Step-by-step explanation:

For a better, clear and unbiased sampling, choosing randomly might not allow for a biased sampling. Choosing in an alphabetical order might not give a representative of the whole hospitals both private and public, thus invigilator the conclusion of our hypothesis test.

Answer:

$275.6

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.

In this question:

[tex]P = 4000, r = 0.08, t = 12[/tex]

Anually:

[tex]n = 1[/tex]

Then

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]A(12) = 4000(1 + \frac{0.08}{1})^{12}[/tex]

[tex]A(12) = 10072.68[/tex]

Quarterly:

[tex]n = 4[/tex]

Then

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]A(12) = 4000(1 + \frac{0.08}{2})^{12*4}[/tex]

[tex]A(12) = 10348.28[/tex]

How much would the future value of the investment increase?

10348.28 - 10072.68 = 275.6

The future value of the investment would increase by $275.6.

Answer:

Acute and equilateral triangle

Step-by-step explanation:

An acute triangle is a triangle in which each of its angles measures less than 90 degrees.

There are three types of acute e triangle

1. Equilateral triangle: This is an acute triangle which has all of its sides equal as in the case of Steve.

2. Isosceles triangle is an acute triangle that has only two equal sides.

3. Scalene triangle is an acute triangle that has no Equal sides, that is, none of its sides are equal.

Answer:

Equilateral triangle

Step-by-step explanation:

Steve's triangle is an acute triangle.

An acute triangle has each of its 3 acute. That is the angles are less than 90°. It could be an equilateral triangle, isosceles or scalene triangle.

In this case, it is an equilateral triangle since all 3 sides (5m) are equal. Therefore all 3 angles of the triangles are equal( angle would be 60°).

Answer:

It cost $0.91 10 years ago.

It takes 10.24 years for the cost of bread to double.

Step-by-step explanation:

The equation for the price of bread after t years has the following format:

[tex]P(t) = P(0)(1+r)^{t}[/tex]

In which P(0) is the current price, and r is the inflation rate, as a decimal.

If we want to find the price for example, 10 years ago, we find P(-10).

Inflation is at a rate of 7% per year. Evan's favorite bread now costs $1.79.

This means that [tex]r = 0.07, P(0) = 1.79[/tex]. So

[tex]P(t) = P(0)(1+r)^{t}[/tex]

[tex]P(t) = 1.79(1+0.07)^{t}[/tex]

[tex]P(t) = 1.79(1.07)^{t}[/tex]

What did it cost 10 years ago?

[tex]P(-10) = 1.79(1.07)^{-10} = 0.91[/tex]

It cost $0.91 10 years ago.

How long before the cost of the bread doubles?

This is t for which P(t) = 2P(0) = 2*1.79. So

[tex]P(t) = 1.79(1.07)^{t}[/tex]

[tex]2*1.79 = 1.79(1.07)^{t}[/tex]

[tex](1.07)^{t} = 2[/tex]

[tex]\log{(1.07)^{t}} = \log{2}[/tex]

[tex]t\log{1.07} = \log{2}[/tex]

[tex]t = \frac{\log{2}}{\log{1.07}}[/tex]

[tex]t = 10.24[/tex]

It takes 10.24 years for the cost of bread to double.

Answer:

  hyperbola

Step-by-step explanation:

A graphing calculator shows the equation is that of a hyperbola.

__

Multiplying by the denominator gives ...

  r(2 -3sin(x)) = 1

  2r -3y = 1 . . . . . . . . substituting y=r·sin(x)

  2r = 1 +3y . . . . . . . .isolating r

  4r² = 1 +6y +9y² . . squaring both sides

  4(x² +y²) = 1 +6y +9y² . . . . . substituting x²+y² = r²

  4x² -5y² -6y -1 = 0 . . . . . . . . general form equation of a hyperbola

A. True, a rhombus is a parallelogram with equal sides. A rhombus has four congruent sides.

B. True, but there are two other ways to find the area of a rhombus: there is the "diagonals" method and the "trigonometry" method.

C. False, the area of a rhombus is not less than the area of a parallelogram because it will depend on the diagonals.

D. False, a parallelogram is not always a rhombus because the dimensions and other attributes of a parallelogram may vary while the rhombus will remain equal for all aspects.

E. True, if you use the base times height formula but if you used any of the other formulas this would be false.

Answer:

8 footballs

18 basketballs

36 baseballs

24 softballs

Step-by-step explanation:

Let f = footballs

f = 8

Let b = basketballs

b = 2+2f = 2 +2(8) = 2 +16 = 18

Let B = baseballs

B = 5f -4 = 5(8) -4 = 40-4 = 36

Let s = softballs

s = 6+1/2B = 6+1/2(36) = 6+18 = 24

The total is 86

f+b+B +s = 86

8+18+36+24 = 86

86=86

There are 8 footballs.

Two more than twice the number of footballs are basketballs:

2f + 2 = b

f = number of footballs

b = number of basketballs

In the first statement, there are 8 footballs. So, f = 8

2(8) + 2 = b

16 + 2 = b

18 = b

Therefore, there are 18 basketballs.

Four less than 5 times the number of footballs are baseballs:

5f - 4 = a

f = number of footballs

a = number of baseballs

In the first statement, there are 8 footballs. So, f = 8

5(8) - 4 = a

40 - 4 = a

36 = a

Therefore, there are 36 baseballs.

Six more than half of the baseballs are softballs:

a/2 + 6 = s

a = number of baseballs

s = number of softballs

In the third statement, there are 36 baseballs. So, a = 36

(36)/2 + 6 = s

18 + 6 = s

24 = s

Therefore, there are 24 softballs.

Best of Luck!

Answer:

The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is 0.8 = 80%.

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Prefers swimming on weekends.

Event B: Being female.

25% prefer swimming on weekends

This means that [tex]P(A) = 0.25[/tex]

It is found that 20% of the members in that city prefer swimming on weekends and are female

This means that [tex]P(A \cap B) = 0.2[/tex]

So

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2}{0.25} = 0.8[/tex]

The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is 0.8 = 80%.

Answer:

5 minutes

Step-by-step explanation:

200+15=215

214/43=5

It moved up a total of 200 + 15 = 215 meters at 43 meters per minute

t = 215 m / (43 m/min) = 5 minutes

Answer: 5 minutes

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is

The management of Discount Furniture, a chain of discount furniture stores in the Northeast, designed an incentive plan for salespeople. To evaluate this innovative plan, 12 salespeople were selected at random, and their weekly incomes before and after the plan were recorded.

Salesperson Before After

Sid Mahone $320 $340

Carol Quick 290 285

Tom Jackson 421 475

Andy Jones 510 510

Jean Sloan 210 210

Jack Walker 402 500

Peg Mancuso 625 631

Anita Loma 560 560

John Cuso 360 365

Carl Utz 431 431

A. S. Kushner 506 525

Fern Lawton 505 619

Solution:

Corresponding income of salespersons before and after form matched pairs.

The data for the test are the differences between the income is salespersons.

μd = the​ income before minus their income after.

Bedore after diff

320 340 -20

290 285 5

421 475 - 54

510 510 0

210 210 0

402 500 - 98

625 631 -6

569 560 0

360 365 - 5

431 431 0

506 525 - 19

505 619 - 114

Sample mean, xd

= (- 20 + 5 - 54 + 0 + 0 - 98 - 6 + 0 - 5 + 0 + - 19 - 114)/12 = - 25.92

xd = - 25.92

Standard deviation = √(summation(x - mean)²/n

n = 12

Summation(x - mean)² = (- 20 + 25.92)^2 + (5 - 25.92)^2 + (- 54 + 25.92)^2+ (0 + 25.92)^2 + (0 + 25.92)^2 + ( - 98 + 25.92)^2 + ( - 6 + 25.92)^2 + (0 + 25.92)^2 + (- 5 + 25.92)^2 + (0 + 25.92)^2 + (- 19 + 25.92)^2 + (- 114 + 25.92)^2 = 17784.5168

Standard deviation = √(17784.5168/12

sd = 38.5

For the null hypothesis

H0: μd ≥ 0

For the alternative hypothesis

H1: μd < 0

1) The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 12 - 1 = 11

2) The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = ( - 25.92- 0)/(38.5/√12)

t = - 2.33

3) We would determine the probability value by using the t test calculator.

p = 0.02

4) Assume alpha = 0.05

Since alpha, 0.05 > than the p value, 0.02, then we would reject the null hypothesis. We can conclude that at 5% significance level, there is a significant increase in the typical salesperson’s weekly income due to the innovative incentive plan

Answer:

  5

Step-by-step explanation:

Solving the given equation for r, we get ...

  y = rx

  y/x = r

Then we can find r from any pair in the table:

  r = 35/7 = 5

The constant of proportionality is 5.

Answer:

y=3

Step-by-step explanation:

i did it in khan academy :)

Answer:

[tex]0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570[/tex]

[tex]0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630[/tex]

The 95% confidence interval for the true proportion would be given by (0.570;0.630) .

And if we convert this into % we got (57.0%, 63.0%)

Step-by-step explanation:

The information given we have the following info given:

[tex] n = 1019[/tex] represent the sampel size

[tex] \hat p=0.6[/tex] represent the sample proportion of interest

The confidence level is 95%, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]

The confidence interval for the mean is given by the following formula:  

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

Replacing the info given we got:

[tex]0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570[/tex]

[tex]0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630[/tex]

The 95% confidence interval for the true proportion would be given by (0.570;0.630) .

And if we convert this into % we got (57.0%, 63.0%)

Answer:

c= 5 yards.

Step-by-step explanation:

4*1.5=6

30/6= 5

As we solve we generate a succession of equivalent equations.

10t - 4t + 3t = 8

9t = 8

t = 8/9

Answer:

10t-4t+3t=8

t (10-4+3)=8

t (9)=8

9t=8

t=8/9

Step-by-step explanation:

In the question stated above, the common factor amongst the numbers with the variables is t, therefore we factorise the t out of the numbers, hence leaving t outside the bracket. After we solve the equation of the simple numbers of which the product is 9. After this we already know the 9 is to be multiplied by the t to make it 9t=8. We divide both side by the 9 and get a result of t=8/9